12 Chapter The Term Structure of Interest Rates
I. Yield Curve
what is the relationship between yield and maturity?
o complicated--sometimes the yield decreases with maturity, sometime it
increases with maturity
o usually the yield rises with maturity but not always
looking at bonds with same properties, except for different maturities
o Treasury securities--many maturities, all liquid, all default-free
Tbills: 1 mo. (4 wk.) , 3 mo. (13 wk.), 6 mo. (26 wk), 1 yr. (52
wk.)
zero coupon
Tnotes: 2, 5, 10 years
coupon
Tbonds: 30 years (not since 2001)
coupon
yield curve is a picture of the term structure (the relationship between yield and
maturity) at a given point in time
o upward sloping yield curve
longer-term bonds have higher yields
o downward sloping yield curve
longer-term bonds have lower yields
o flat yield curve
yields do not vary with maturity
o changing slope yield curve
yield/maturity relationship is not consistent
II. Theories of the Term Structure
Pure Expectations Theory (broad interpretation)
o assume
bonds of different maturities are perfect substitutes (investors care
only about total return)
o implication
long term bond yields are the average of current and expected
future short term bond yields
approximately an arithmetic average
exactly a geometric average
why? because if investors expected long term bonds to
have a better yield, then they would only hold long term
bonds (because they are indifferent among maturities); if
they expected short-term bonds to do better they would
only hold short term bonds. Since we observe that
investors hold both short and long term bonds then it must
be the case that they expect them to yield about the same.
this argument ASSUMES that investors have no
preference for short or long term bonds
o
so the slope of the yield curve indicates
investors expectations of future interest rates
the yield curve slopes up, rates
are expected to rise, if the yield curve
slopes down, rates are expected to fall
o How does the expectations theory compare to reality?
the yield curve usually slopes up but
the expectations theory cannot explain this--it would
predict an upward slope only about 50% of the time.
What's the problem with the expectations the theory?
assumption that bonds of different maturities are perfect
substitutes is not realistic:
long term bonds carry greater interest rate risk or
price risk than short term bonds
short term bonds carry greater reinvestment risk than
long term bonds
Liquidity Theory
o assume
bonds of different maturities are imperfect substitutes and that
investors prefer short term bonds to long term bonds
long term bonds must include a positive liquidity premium over
and above expected future short term interest rates
o implication
long term bond yields = average of short term yield + liquidity
premium
this make the yield curve much more difficult to interpret, because
its slope now depends on two things, and we do not know the size
of the premium, only its sign
an upward sloping yield curve could mean that interest
rates are expected to rise, if the liquidity premium is small
OR it could mean that interest rates are expected to stay the
same if the liquidity premium is large.
the liquidity theory DOES explain why the yield curve usually
slopes up--since long term bond yields include a liquidity
premium that is positive, they are likely to be larger than short
term bond yields
The Preferred Habitat Theory
o assume
bonds of different maturities are imperfect substitutes and that
investors prefer short term bonds to long term bonds sometimes,
but sometimes they prefer long term bonds to short term bonds
the liquidity premium can be positive or negative
o implications
the yield curve under this theory is even more difficult to interpret
since we know neither the sign nor the size of the liquidity
premium.
o most evidence suggests that the liquidity premium is almost always
positive.
The Market Segmentation Theory
o assume
bonds of different maturities are NOT substitutes at all.
the long term and short term bond markets are separate or
segmented.
o implications
long and short term bond yields are not related, so the slope of the
yield curve does not signal anything about future short-term
interest rates.
long and short-term yields are determined by supply and demand
in totally separate markets
o it is very unlikely that investors are always unwilling to substitute across
maturities